/*
The gray code is a binary numeral system where two successive values differ in only one bit.

Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code. A gray code sequence must begin with 0.

For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:

00 - 0
01 - 1
11 - 3
10 - 2
Note:
For a given n, a gray code sequence is not uniquely defined.

For example, [0,2,3,1] is also a valid gray code sequence according to the above definition.

For now, the judge is able to judge based on one instance of gray code sequence. Sorry about that.
*/

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> result(1, 0);
        for (int i=1; i<=n; i++) {
            vector<int> tmp = result;
            reverse(tmp.begin(), tmp.end());
            // prepend '1' at bit i
            for (int j = 0; j < tmp.size(); j++) {
                result.push_back(tmp[j] | (1<<(i-1)));
            }
        }
        return result;
    }
};
